Some factors that greatly impact the utility of an imaging system include resolution, signal-to-noise ratio (SNR), field of view (FOV), and the number of images that the imaging system can capture. Resolution determines the highest amount of image detail that can be captured in a scene and is fundamentally limited by the aperture size of the optical system (see Introduction to Fourier Optics by Joseph Goodman, McGraw-Hill, second edition, 1996). One calculation of aperture size employs a modulation transfer function (MTF). The MTF for an incoherent diffraction-limited optical system is essentially the aperture's MTF, which is calculated by autocorrelating the aperture function. For a clear circular aperture of diameter D, the incoherent aperture MTF is given by:                                                        MTF              incoherent                        ⁡                          (              ρ              )                                =                                    2              π                        ⁡                          [                                                                    cos                                          -                      1                                                        ⁡                                      (                                          ρ                      n                                        )                                                  -                                                      ρ                    n                                    ⁢                                                            1                      -                                              ρ                        n                        2                                                                                                        ]                                      ⁢                                  ⁢                              for            ⁢                                                   ⁢            0                    ≤                      ρ            n                    ≤          1                                    (                  Equation          ⁢                                           ⁢          1                )             MTFincoherent(ρ)=0 for ρn>1  (Equation 2)where                               ρ          n                =                  ρ                      ρ            c                                              (                  Equation          ⁢                                           ⁢          3                )                                          ρ                      c            ⁡                          (              incoherent              )                                      =                              1                          λ              ⁡                              (                                  f                  ⁢                  #                                )                                              =                      D                          λ              ⁢                                                           ⁢              f                                                          (                  Equation          ⁢                                           ⁢          4                )            where ƒ is the focal length of the optical system, ƒ#≡ƒ/D, λ is the wavelength of the electromagnetic wave, and ρ is the radial spatial frequency. For coherent imaging systems with circular apertures, the MTF is simply the aperture function:MTFcoherent(ρ)=1 for 0≦ρn≦1  (Equation 5)MTFcoherent(ρ)=0 for ρn>1  (Equation 6)where                               ρ                      c            ⁡                          (              coherent              )                                      =                              1                          2              ⁢                              λ                ⁡                                  (                                      f                    ⁢                    #                                    )                                                              =                      D                          2              ⁢              λ              ⁢                                                           ⁢              f                                                          (                  Equation          ⁢                                           ⁢          7                )            Note that for both coherent and incoherent imaging systems there is a distinct spatial frequency cutoff, ρc, which is proportional to the aperture size and defines the highest spatial resolution that can be imaged with the optical system. An imaging system with a larger aperture size, therefore, will capture images at higher resolution than an imaging system with a smaller aperture size.
Sparse apertures (also termed diluted apertures) use a reduced aperture area to synthesize the optical performance of a filled aperture. An optical system employing sparse apertures can combine the light captured by smaller apertures to capture a higher spatial resolution than possible from any of the individual apertures. This concept is very appealing in technology areas where a filled aperture is too large or heavy for the intended application. Sparse aperture concepts have been used to design large astronomical telescopes, such as the multiple mirror telescope in Arizona, as well as small endoscopic probes (see U.S. Pat. No. 5,919,128 by Fitch issued Jul. 6, 1999, titled “SPARSE APERTURE ENDOSCOPE”). Prior art sparse aperture systems that use multiple apertures to improve the resolution of the images have not had the versatility to take advantage of other benefits that can be obtained from multiple aperture systems.
FIG. 1a illustrates a traditional Cassegrain telescope 10. FIG. 1b illustrates a prior art sparse aperture telescope 12 created by removing parts of the primary mirror of the Cassegrain telescope 10 in FIG. 1a. FIG. 1c illustrates a prior art sparse aperture telescope 14 created by using multiple afocal telescopes 16 that relay light into a combiner telescope 18 using an optical relay system 20 to precisely ensure that the light from each telescope arrives at a detector 21 simultaneously.
In general, a signal, measurable in the number of photons that reach the detector 21, from a scene being imaged by an optical system, is                     signal        =                                                            A                detector                            ⁢                              π                ⁡                                  (                                      1                    -                    ɛ                                    )                                            ⁢                              t                int                                                    4              ⁢                                                (                                      f                    ⁢                    #                                    )                                2                            ⁢              hc                                ⁢                                    ∫                              λ                min                                            λ                max                                      ⁢                                                            L                  scene                                ⁡                                  (                  λ                  )                                            ⁢                              τ                optics                            ⁢              λ              ⁢                                                           ⁢                              ⅆ                λ                            ⁢                                                           ⁢                              (                photons                )                                                                        (                  Equation          ⁢                                           ⁢          8                )            where Adetector is the area of the detector, ε is the fraction of the optical aperture area obscured, tint is the integration time of the imaging system, h=6.63×10−34 (j−s), c=3×108 (m/s), λmin and λmax define the spectral bandpass, Lscene is the spectral radiance from the scene, and τoptics, is the transmittance of the optics. Random noise, for example photon noise, arising from elements adds uncertainty to the signal level of the scene. Consequently random noise is quantified by the standard deviation of its statistical distribution, σ. The signal-to-noise ratio (SNR) is the ratio of the signal level to the noise level, i.e.                               SNR          ≡                      signal            noise                          =                  signal          σ                                    (                  Equation          ⁢                                           ⁢          9                )            If the photon noise from the scene is the dominant noise source, then the SNR is given by:                     SNR        =                              signal            σ                    =                                    signal                              signal                                      =                          signal                                                          (                  Equation          ⁢                                           ⁢          10                )            because the photon noise follows a Poisson distribution of the signal, i.e. the variance of the noise equals the mean signal. If the SNR is not sufficient, then increasing the signal level from the scene relative to the noise will increase the SNR and improve the image quality. Increasing the integration time will increase the signal level, but this can introduce motion blur in the image if the imaging system moves relative to the scene or an object. Multiple short-exposure images of the same scene can be acquired by a single camera and summed together to increase the signal level without introducing motion blur. However, if the camera can only acquire one image at a time, there will be a time difference between the multiple images, which could introduce unwanted image artifacts.
The field of view (FOV) of an imaging system determines the area of the scene that can be acquired in a single image. FIG. 2 illustrates an image capture system, such as a camera, including an imaging element 22 having a focal length f, wherein the focal length is a property of the imaging element 22, and an imaging sensor 24. A scene 26 at a distance do in front of the camera will be properly focused at the imaging sensor 24 at a distance di behind the imaging element 22, if the relationship between do, di, and f is                                           1                          d              o                                +                      1                          d              i                                      =                  1          f                                    (                  Equation          ⁢                                           ⁢          11                )            The field of view (FOV) describes the angle subtended by the imaging sensor 24, given by                     FOV        =                  2          *                                    tan                              -                1                                      ⁡                          (                                                L                  sensor                                                  2                  ⁢                                      d                    i                                                              )                                                          (                  Equation          ⁢                                           ⁢          12                )            where Lsensor is the length of the imaging sensor 24. The length of the scene 26 captured by the imaging sensor 24 is given by:                                           L            scene                    =                                                                      d                  o                                                  d                  i                                            ⁢                              L                sensor                                      =                                          (                                                                            d                      o                                        f                                    -                  1                                )                            ⁢                              L                sensor                                                    ⁢                                  ⁢                                            If              ⁢                                                           ⁢                              d                o                                      ⪢            f            ⪢                          L              sensor                                ,          then                                    (                  Equation          ⁢                                           ⁢          13                )                                          L          scene                ≅                                            d              o                        f                    ⁢                      L            sensor                          ≅                              d            o                    ⁢          FOV                                    (                  Equation          ⁢                                           ⁢          14                )            Increasing the size of the imaging sensor 24 will increase the FOV and the area of the scene 26 imaged, but there are usually limitations to the size of imaging sensor 24 that can be used, due to manufacturing constraints and the image quality of the optical system off-axis. The FOV is usually increased by increasing do or by decreasing f, both of which decrease the scale of the image and reduce the resolution. The FOV, therefore, generally involves a trade between resolution and the area of the scene 26 imaged.
The field of regard is the area in the scene 26 within which the image capture system can acquire an image. The field of regard is generally larger than the FOV and is determined by the image capture system's capability to view certain areas of the scene. A single imaging sensor 24 may take a long time to acquire multiple images within the field of regard.
There is a need, therefore, for a multiple aperture image capture system that can improve the resolution, produce a higher signal image, image a larger FOV, and/or improve the number of images acquired per unit time.